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We propose CA-Sinkhorn-DRO, a class-aware distributionally robust framework for few-shot domain adaptation that wraps each class-conditional source measure in its own Sinkhorn ball and imposes an explicit \(\ell _1\) -band on the class prior. This decoupling of label-shift and covariate-shift uncertainty yields a minimax learner with a provable \(\mathcal {O}\bigl ((d+\log K)/\sqrt{n}\bigr )\) excess-risk bound, which tightens to \(\mathcal {O}\bigl ((n+m)^{-1/2}\bigr )\) when unlabelled target data are available. To solve the resulting DRO efficiently on high-dimensional embeddings, we develop a low-rank Nyström Sinkhorn solver that achieves a \(12\times \) speed-up with negligible accuracy loss. Empirically, CA-Sinkhorn-DRO outperforms competitive OT-based baselines by +4–8 pp on Office-Home, DomainNet, CIFAR \(\rightarrow \) STL, and PACS, produces tight risk certificates that track actual errors, and remains robust to hyperparameter choices.

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Class-Aware Sinkhorn-DRO for Few-Shot Domain Adaptation

  • 会议论文

  • 发表日期：

    2025年

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  • Thomas Y. Chen

摘要

We propose CA-Sinkhorn-DRO, a class-aware distributionally robust framework for few-shot domain adaptation that wraps each class-conditional source measure in its own Sinkhorn ball and imposes an explicit \(\ell _1\) -band on the class prior. This decoupling of label-shift and covariate-shift uncertainty yields a minimax learner with a provable \(\mathcal {O}\bigl ((d+\log K)/\sqrt{n}\bigr )\) excess-risk bound, which tightens to \(\mathcal {O}\bigl ((n+m)^{-1/2}\bigr )\) when unlabelled target data are available. To solve the resulting DRO efficiently on high-dimensional embeddings, we develop a low-rank Nyström Sinkhorn solver that achieves a \(12\times \) speed-up with negligible accuracy loss. Empirically, CA-Sinkhorn-DRO outperforms competitive OT-based baselines by +4–8 pp on Office-Home, DomainNet, CIFAR \(\rightarrow \) STL, and PACS, produces tight risk certificates that track actual errors, and remains robust to hyperparameter choices.